Related papers: An Explicit Fourth-Order Hybrid-Variable Method fo…
In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising in the $2D$ Oldroyd model of viscoelastic fluids of order one with the forcing term…
A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In…
We present a divergence-free and $H(div)$-conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving stationary incompressible viso-resistive magnetohydrodynamic…
In this study, a stabilized finite element analysis of unified Stokes-Darcy-Brinkman system fully coupled with variable coefficient Advection-Diffusion-Reaction equation(VADR) has been carried out. The viscosity of the fluid, involved in…
The present work is devoted to introduce the backward Euler based modular time filter method for MHD flow. The proposed method improves the accuracy of the solution without a significant change in the complexity of the system. Since time…
We describe an algorithm, based on Euler's method, for solving Volterra integro-differential equations. The algorithm approximates the relevant integral by means of the composite Trapezium Rule, using the discrete nodes of the independent…
We present a novel high-order nodal artificial viscosity approach designed for solving Magnetohydrodynamics (MHD) equations. Unlike conventional methods, our approach eliminates the need for ad hoc parameters. The viscosity is…
In this paper we develop a fully nonconforming virtual element method (VEM) of arbitrary approximation order for the two dimensional Cahn-Hilliard equation. We carry out the error analysis for the semidiscrete (continuous-in-time) scheme…
This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully nonlinear partial differential equations (PDEs) in 1-D. The…
In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved.…
The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular…
We propose a modification of the standard linear implicit Euler integrator for the weak approximation of parabolic semilinear stochastic PDEs driven by additive space-time white noise. The new method can easily be combined with a finite…
We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
In this paper we establish a stability barrier of a class of high-order Hermite-type discretization of 1D advection equations underlying the hybrid-variable (HV) and active flux (AF) methods. These methods seek numerical approximations to…
In this paper we consider multi-dimensional partial differential equations of parabolic type involving divergence form operators that possess a discontinuous coefficient matrix along some smooth interface. The solution of the equation is…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…
We propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld, J. Sch\"oberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
Among the single-trajectory Gaussian-based methods for solving the time-dependent Schr\"{o}dinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller's original thawed Gaussian approximation, it…